A common operation in signal processing is signal integration. Such an operation may be depicted by a plot in which the x-axis represents either time or a parameter which affects the signal intensity, which may be referred to as the y-axis response, as shown in FIG. 1. To recover the entire signal, the y-axis signal intensity is summed along a section of the x-axis. This type of integration is commonly referred to as the “trapezoid rule.”
Another approach to integration is through the use of curve fitting. In this method, as depicted in FIG. 2, a section of the intensities along the x-axis is examined, and a mathematical formula is used to iteratively make a combined curve of the shape matching a signal 202. A curve area 208 is then determined by summing the areas of the iterative mathematical functions 204, 206.
The trapezoidal rule method is somewhat simpler to implement for digitized signals when the desired signal is isolated because no assumptions are made concerning the underlying mathematical functions that describe the peak. In such a case, baseline points are defined such as to be outside the signal boundaries, and signal summation is carried out at points equal to or internal to a baseline region, as shown in FIG. 3. In FIG. 3, outer lines 302, 304 denote baseline start and stop points, respectively, and inner lines 306, 308 denote integration start and stop points, respectively. A net signal 310 is the light shaded area after a baseline area 309 has been subtracted.
In certain signal processing applications, however, it is possible for peak positions associated with measured quantities to shift slightly. Such a shift may be caused by environmental temperature change over time that change the physical position of components within a spectrometer. Specific to Raman spectroscopy, the excitation laser wavelength (i.e., wavenumber) may drift over time. Aside from these instrumental effects, the molecular nature of Raman spectroscopy may cause peaks to shift due to composition changes in a mixture and/or temperature changes of the sample. In conventional signal integration, the baseline and integration limits remain constant, but the peak may shift relative to the integration limits to such an extent that the integration limits are no longer optimal, resulting in errors in determining a concentration of a constituent of a sample under test. Accordingly, there exists a need for curve integration techniques that do not rely on absolute parameters.